Is there an egress window or exterior door in the "bedroom". Double Stud Walls (offset) with Quiet Rock, Sound Deadening Insulation and caulk every joint and seam, and or Green Glue should help but as far as sound-proof, not sure

As above, but going double stud is extreme if you are already using Green Glue or acoustically engineered drywall such as Quiet Rock, Silent FX or Soundbreak XP. Carpeting in the bedroom above will greatly reduce the impact sound travelling down.

@millworkman Yes there is an egress window but no exterior door. I know I would not be able to get it completely sound-proof but being able to reduce the noise (at least coming from the furnace, the rooms being over top of one another isn't as much of an issue) as much as possible is preferred.

@worthy Good point on the carpet but it simply cannot be done. I have quite a few allergies including one to my cats (haha!) so there is zero carpeting in my house to help keep me sane. :P

Depends on how much you want to spend and how "Sound Proof" you would like it to be. Here is a good link explaining STC and to what level you are trying to accomplish. http://www.soundproofingcompany.com/soundproofing101/understanding-stc/

Most of our clients, we end up insulating the wall, installing sound board, and two layers of sheetrock with a sound channel. the small details in this are important also. Such as if there is a door in the wall, etc.